The following model is sometimes used to model the spread of a contagious diseas
ID: 3046799 • Letter: T
Question
The following model is sometimes used to model the spread of a contagious disease. Suppose a box contains b black and r red marbles. A marble is drawn and c marbles of that color together with the drawn marble are replaced in the box before the next marble is drawn, so that infected persons infect others while immunity to the disease may also increase. (a) Find the probability that the first three marbles drawn are red. (b) Show that the probability of drawing a black on the second draw is the same as the probability of drawing a black on the first draw.Explanation / Answer
Total number of marbles = 12+8+12 = 32
a. P(first 3 are red) = (8/32) * (7/31) * (6/30) = 7/620 = 0.0113
b. P(second draw is black) = P(1st is black) * P(2nd is black | 1st is black) + P(1st is non-black) * P(2nd is black | 1st is non-black)
= 12/32 * 11/31 + 20/32 * 12/31
= 3/8 = 0.375
P(first is black) = 12/32 = 3/8 / 0.375
Hence, P(second draw is black) = P(first is black)
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